The invention is based on a device for measuring the mass of a flowing medium. A device of this kind has already been disclosed (DE-OS 195 24 634), having a plate-shaped sensor element accommodated in a recess of a sensor support, and having a sensor region with at least one measurement resistor that is exposed to the flowing medium. The sensor element is partially glued in the recess by means of adhesive and has a contacting region for connection to the at least one active measurement region of the sensor element, and connecting lines lead from this contacting region to an evaluation circuit. The sensor element is mounted in the recess, essentially flush to the wall, in order to obtain a flow at the sensor element without flow separations. Between the sensor element and the walls of the recess, there is a manufacture-conditional gap that cannot be totally prevented for tolerance reasons. Furthermore, the electronic elements of the evaluation circuit as well as the connecting lines to the contacting region of the sensor element must be protected against moisture of the kind that can occur in the operation of the device in a motor vehicle.